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In this paper, we establish the solution of the fourth-order nonlinear homogeneous neutral functional difference equation. Moreover, we study the new oscillation criteria have been established which generalize some of the existing results of the fourth-order nonlinear homogeneous neutral functional difference equation in the literature. Likewise, a few models are given to represent the significance of the primary outcomes.

The manufacturing sectors are consistently striving to figure out ways to minimize the consumption of natural resources through rational utilization. This is achieved by a proper understanding of every minute influence of parameters on the entire process. Understanding the influencing parameters in determining the machining process efficacy is inevitable. Technological advancement has drastically improved the machining process through various means by providing better quality products with minimum machining cost and energy consumption. Specifically, the machining factors such as cutting speed, spindle speed, depth of cut, rate of feed, and coolant flow rate are found to be the governing factors in determining the economy of the machining process. This study is focused on improving the machining economy by enhancing the surface integrity and tool life with minimum resources. The study is carried out on low-carbon mold steel (UNS T51620) using Box–Behnken design and grey regression analysis. The optimized multiobjective solution for surface roughness (Ra), material removal rate (MRR), and power consumed (Pc) and tool life is determined and validated through the confirmatory run. The optimized set of parameters in Box–Behnken design and grey regression analysis with that of confirmatory runs shows a 10% deviation that proves the reliability of the optimization techniques employed.